1. Field of the Invention
This invention relates to a system and method for receding-horizon adaptive and reconfigurable control.
2. Brief Description of the Prior Art
It has long been a goal of flight-control research to achieve first-rate flying qualities for military aircraft across constantly expanding operational envelopes of altitude, Mach number, angle of attack, maneuver accelerations, and stores configurations. Simultaneously, there has been an interest in reducing the time and cost for developing new flight control systems. In recent years, attention has also focused on flight-control system robustness, i.e., the ability to operate well under off-nominal or unexpected conditions. The emphasis on robustness has led, logically, to studies of reconfigurable control, which is intended to adapt quickly to control surface malfunctions, effector impairments, or damage to the aircraft, as well as less traumatic events such as release of stores or gradual component-hardware aging.
The often conflicting objectives of improved aircraft performance and lowered cost have focused attention on the flight-control discipline because control-system development can be costly, particularly with short aircraft production cycles. To hand-tailor flight-control designs to meet desired flying-qualities requirements over all flight conditions in the operational envelopes of high-agility aircraft typically involves multiple design iterations.
It also becomes a challenge to create reliable algorithms to reconfigure flight-control systems quickly and effectively should impairments occur. Traditional control synthesis methods are tedious, requiring specialized knowledge, substantial off-line analysis, and extensive in-flight validation (often accompanied by numerous iterations of large and complex pre-specified gain schedules). These difficulties are compounded when one attempts to design for the large universe of possible anomalies that may be experienced during the flight-vehicle service life. Many reconfigurable control design methods attempt to compensate for potential impairments and off-nominal operating conditions by combining multiple highly-specialized off-line designs with on-line failure detection algorithms. If and when a specific class of failure is isolated, a separate control system, designed to compensate for the given failure, is invoked and used thereafter.
Rather than rely on numerous control system implementations based on pre-hypothesized impairment or airframe damage scenarios, a number of researchers have been developing reconfigurable controllers based on adaptive control techniques. Many of these are direct-adaptive approaches whereby control gains are adjusted based on system performance. Recently, however, a number of researchers have been investigating indirect-adaptive control approaches whereby a modern control law and on-line parameter identification algorithm are designed independently. Such approaches, while requiring the identification of many parameters, can leverage existing and future research in the areas of optimal model-following control and robust parameter identification.
Whereas many control applications are focused on achieving desired steady-state responses, flight control is interested in optimal transient response. Model predictive control (MPC) is well suited to achieve these transient performances.
Model predictive control was originally developed in the process controls industry under a variety of names, the most common of which is generalized predictive control (GPC). There are a number of variations of GPC methodologies, including discrete and continuous time versions, tracking formulations, and adaptive algorithms that combine the GPC algorithm with an on-line system identification technique. However, all of the variants work in very much the same way. First, a finite time optimal control solution is computed using a quadratic cost function, a model of the current plant dynamics, the current system states, and a model of the desired plant response over the horizon. Once the open-loop sequence of optimal control commands are determined, the first command, corresponding to the current time, is applied to the system. At the next control update, rather than applying the second command in the open-loop optimal command sequence, the finite horizon optimization is completely redone using a new estimate of the plant dynamics, current system states, and desired control. In this way, the open-loop finite-horizon optimal control problem becomes a closed loop problem, and the optimization horizon is said to "recede" because the controller never applies the commands corresponding to the end of the horizon.
A model predictive controller shares a number of advantages with linear quadratic (LQ) control techniques, especially stability and robustness. However, unlike infinite-time LQ control, a receding-horizon controller can anticipate desired plant responses and better account for time-varying plant characteristics. These two qualities make this approach extremely attractive for a number of multi-input multi-output (MIMO) control problems where one is interested in achieving desired transient responses. In fact, it has recently been argued that, for problems that are not inherently linear-time-invariant (LTI), receding-horizon control is the only viable controller synthesis method.
Due to the computational complexity of MPC, MPC has been most successfully applied to processes, such as chemical process control, where slow update rates are allowed for the control computations. Recently, however, with advances in computing technology, MPC-type controllers have been applied to aerospace applications. An adaptive version of receding-horizon optimal (RHO) (RHO refers to the particular receding-horizon controller developed for inner-loop flight control) control has been derived and applied to MIMO three degrees-of-freedom (3DOF) inner-loop aircraft control. In the aeronautical context, the RHO control law accounts for plant nonlinearities by linearizing the aircraft equations of motion at each instant in time and deriving the finite-horizon optimal control strategy for the linearized plant dynamics. Thus, time-varying nonlinear plants are converted to time-varying linear plants, enabling the on-line closed-form derivation of a robust control strategy. Such a strategy is also extremely well suited for reconfigurable control when combined with on-line system identification. Under a recent program, (Neural Network Flight Control System for High-Agility Air Combat) real-time piloted simulations were used to show that an RHO control law can effectively account for plant nonlinearities that occur during high-angle-of-attack and post-stall maneuvering such as velocity vector rolls.
However, the need exists for adaptive and reconfigurable control of aircraft and other complex objects and processes such as, without limitation thereto, chemical plants, electrical power distribution networks, and machines for positioning and locomotion of loads. These complex objects and processes, including their control effectors, will be referred to herein categorically as "plants." In the technical control of many such plants, the major needs are:
1. maintain close tracking of varying input commands or changing set points, including commands computed via input reference models; PA1 2. adapt to changing properties of the plant; in particular, adapt the control law rapidly (reconfigure) for damage or malfunctions of the plant; PA1 3. maintain stability under all conditions, including displacement and/or rate saturation of effectors; PA1 4. optimally allocate control authority among multiple effectors in the context of multi-loop control objectives; PA1 5. minimize costs of control system ownership and operation via reducing design efforts and control law tuning, optimizing use of control energy, achieving survivability under many conditions of plant damage and/or malfunction, realizing faster/more accurate command tracking, and providing economical implementation of the control law. PA1 (a) the current values of the Riccati gains are used to compute the control command, PA1 (b) the desired plant response being used by the Riccati equations is updated, and PA1 (c) integration of the Riccati equations is continued from the current gain set (i.e., the system does not reset them using the variational calculus transversality conditions). PA1 1. cruise flight conditions where the surface and state commands are essentially constant for extended durations of time, PA1 2. constant linear state feedback where the effector commands are linear combinations of the states, or PA1 3. controllers that use "ganged" effectors (e.g., combine both asymmetric flap and asymmetric tail to generate rolling moment).
Indirect adaptive control can achieve many of these objectives. However, for complex processes, there are a number of technical challenges. These are:
1. The number of parameters that must be identified by an indirect adaptive controller is greater than that required by direct adaptive controllers. However, most real-time parameter identification techniques (e.g., Recursive Least Squares, Kalman Filter, etc.) break down due to data collinearities that arise as a result of state feedback, effector ganging, and long periods of straight and level flight.
2. Optimal control approaches, such as linear quadratic regulator (LQR), linear quadratic Gaussian (LQG), and H.sub..infin. optimize over an infinite time horizon and, thus, concentrate on controlling the steady-state characteristics of the closed-loop system. As such, there is an inherent phase-lag in the transient response, and they cannot provide effector commands that anticipate the desired response.
3. Pure multi-input multi-output receding-horizon control approaches, such as MPC and GPC, require numerous and computationally expensive integrations of Riccati differential or Riccati difference equations (or computation and solution of the Diophantine equations).
The prior art teaches a rigorous theory for two-point boundary-value optimal control. The realization of practicable systems implementing this theory has proven difficult because of the extensive computational burdens imposed by the theory.
With reference to initial-value control, it has been proposed that costate differential equations be continuously integrated forward along with the application of effector commands that are likewise derived from the Euler-Lagrange necessary conditions of the variational calculus. It also has been proposed that high-pass filtering of the costate time-variations be used to ensure the long-term stability of the costates while preserving their transient integrity. The compromise in that proposal is to ignore application of the transversality conditions and solve instead an initial-value problem.